Efficient inference of quantum system parameters by approximate Bayesian computation

The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. In quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space with the system size. As the statistics of the measurement data observed—i.e., the —can no longer be easily computed, common approaches such as maximum-likelihood estimators or particle filters become impractical. To address this issue, we propose the use of the approximate Bayesian computation (ABC) algorithm, which evades likelihood computation by sampling from a library of measurement data— prepared for a given quantum device. We apply ABC to interpret photodetection click patterns arising from real-time probing of a two-level atom and an optomechanical system. For the latter, we consider both linear and nonlinear regimes to show how to tailor the ABC algorithm by understanding the quantum measurement statistics. Our work demonstrates that fast parameter inference may be possible regardless of the complexity of the quantum device and the measurement scheme involved.